A lot of new visitors have trouble entering math on the forum. It ought to be easy to add some more descriptive help text to the formatting options below the post. Could it say something like

To use (La)TeX mathematics in your post, make sure “Markdown+Itex” is selected and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted; see here for a list.

?

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Geometry of Shapes and Physicshttps://nforum.ncatlab.org/discussion/8265/
https://nforum.ncatlab.org/discussion/8265/Wed, 31 Jan 2018 20:59:24 -0500gomcarmmateo
What we all probably know is one of Grothendieck's late projects, namely a new foundations of topology "Geometry of Shapes", what we didn't know is that the major motivation was the foundations of space in physics. I am trying to collect relevant literature and reference about "Geometry of Shapes" and typing the project into LaTeX (Grothendieck had intended to publish this research).

I would like to know the great nForum community of "categorical physics" would be interested in contribute. Give it a chance and take a look into the project https://github.com/gcarmonamateo/GeomFormes and hopefully caught your interest in it.

I am aware of the following: in the context of synthetic differential geometry (SDG) one obtains a Lie algebra by exponentiating a microlinear group by a standard infinitesimal object and taking the infinitesimal commutator, and that the functor expressed by this operation factors through formal group laws (FGLs) in the usual way. This reveals that Lie groups are FGLs with respect to first-order infinitesimals.

Now I would like to consider a lined topos equipped with higher-order infinitesimals, and develop in this context a modified notion of microlinearity. I have not yet developed the details of this. But does modifying microlinearity in this way, to yield R-modules by exponentiating FGLs with higher-order infinitesimals, sound reasonable? It is worth saying that in general we want certain polynomial identities to hold in the resulting R-modules, e.g. the Jacobian identity.

While FGLs have been thought of in this way (e.g. Didry in [1], an attempt to extend Lie theory to include Leibniz algebras), I have not found sources discussing modifications of microlinearity to subsume FGLs in the language of SDG. Some suggestive remarks can be found in Nishimura’s work, such as in the introduction of the paper [2], where the author discusses prolongations of spaces with respect to polynomials algebras as generalizations of Weil algebras. What do you think, nForum?

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How to ascertain whether an nLab article with short name already has a "Latest Changes" thread?https://nforum.ncatlab.org/discussion/7908/
https://nforum.ncatlab.org/discussion/7908/Sat, 15 Jul 2017 16:29:38 -0400Peter Heinig

Hopefully, the discussion topic says it all. In particular, this is about

In account->Notification options->Notify me, when comments are posted in my own discussions, when the checkbox is activated the green diamonds start to indicate that the request is sent but it continues in this state indefinitely long (for me, win 10, chrome 49).

Could we add a note next to the comment-entry box telling people that they can use the syntax [[page name]] to link to pages from the nLab from the nForum? Newcomers always have to be told that, and of course, because how else would they know?

Every now and then some spam gets through the filters on the forum. Toby and I can remove it from public view (it stays in the database so if it turns out that it wasn't spam it can easily be deleted). Also, I can set the user account which was used to "banned" to prevent it being used again. Other useful information, such as IPs and email addresses, is also logged. But to keep the place clean, we need to be aware of the spam occurring. I, in particular, don't read every post made here on the forum. So if you spot some spam, please alert someone. Use this discussion if you like.

Here’s something that confuses me about the “tags” on the nForum. Can a tag contain spaces? The comment “(comma separated)” on the tags input box suggests that spaces in a tag would be okay (in particular, wouldn’t break it into two tags), but I don’t think I see any tags containing spaces in the tag cloud.

Have you all considered making an nlab chatroom? It seems that there’s enough frequent interaction on the forum that such a thing would be decently populated. I know I’d certainly spend some time in there! I have no idea what the technical challenges associated to this might be, so perhaps it’s beyond the scope of the people running the nlab and nforum, but it seems a natural next step.

Anyway… just an idea. If there was a chat room I would have just mentioned this in there. Or I guess I wouldn’t have. Uhoh, I’ve confused myself again.

I happened to notice today that there are problems with the proof of Lemma 1. Unfortunately, I do not have time to fix this myself, but I thought I’d let you know.

It can be fixed as follows.

1) Define X^\hat{X} to be the pullback of f×id:X×Y&rightarrow;Y×Yf \times id : X \times Y \rightarrow Y \times Y and the map YI&rightarrow;Y×YY^{I} \rightarrow Y \times Y which is currently denoted (I would not use this notation myself!) by (d0,d1)(d_0,d_1).

2) The required map p:Z&rightarrow;Yp : Z \rightarrow Y is the composite of the map Z&rightarrow;X×YZ \rightarrow X \times Y which is part of the pullback of 1), and the projection map X×Y&rightarrow;YX \times Y \rightarrow Y.

3) The required fibration Z&rightarrow;XZ \rightarrow X arises in the same way as in 2), but composing with the the other projection map instead,

It’s been getting a little lonely here, recently. Somehow I suspect it’s not unrelated to a flood of physics-related posts that I am making, to which maybe none of the regulars here can – or probably wants to – connect? – except notably David Corfield, that is.

There is hope, though: Before long I’ll be posting a lot about stable homotopy theory, when our group seminar starts again. I bet that will trigger more reactions around here… at least if anyone is still left by then.

Here is the actual question that I have, concerning the reception of physics-related posts among the nn-crowd:

a while back Davic C. had published an interview that he did with me in this issue.pdf of “The Reasoner”. In that interview, I believe, I had tried to say something about the relation of physics to topics more manifestly in the nn-arena. That need not mean much, but in my memory what was unusal was that something I said back then managed to transmit some spark, and right afterwards I was contacted by some more pure mathematicians expressing interest in this kind of connection.

Notably, I seem remember Todd Trimble here (hi Todd! :-) to come back from reading that interview and expressing the desire to dive into cohesive homotopy type theory due to some – if I remember correctly – “excitement” that something which I said in the interview did induce. Am I remembering that correctly? Sorry if I am hallucinating. I am not sure how to search for the thread where this happened.

I think back then I had the bad taste to react to that by being busy with some task and promising to join into the project of expanding the entry on cohesive homotopy type theory later. That was probably stupid of me and a lost opportunity. Not sure what happened.

In any case, what I am wondering is: does anyone here – in addition to David C. that is – see a chance to be re-ignited by that spark, if it was one, find some interest in the application of higher cohesive topos theory to quantum physics and by jointly exploring this make the nForum here a more lively and more rewarding place… as it maybe was a while back when we were all throwing around more pure category theory?